An unarmed Army National Guardsman was pulled over on a Queens road and fatally shot by an elite NYPD officer yesterday — and the DA now is probing what the victim’s friend called a case of police “road rage.”

Noel Polanco’s hands were on the steering wheel of his 2012 Honda Fit moments before Detective Hassan Hamdy shot him once in the torso, a woman sitting in the front passenger seat told cops and reporters.

But police spokesman Paul Browne said it’s unknown if Polanco, 22, moved after Hamdy yelled, “Show me your hands!” to the three people in the car, one a sleeping off-duty cop in the back seat, on the Grand Central Parkway near La Guardia Airport at 5:15 a.m.

No weapon was found in the car. An electric drill was on the driver’s-side floor.

“The matter is under investigation,” said a spokeswoman for DA Richard Brown. NYPD Internal Affairs is also investigating.

Polanco’s pal Diane DeFerrari, a bartender who was in the front seat, last night accused cops of killing him in “an act of road rage” after he cut off the cops’ unmarked car, not knowing who they were.

“There was no reason for this innocent to be killed,” DeFerrari said. “He was shot intentionally.”

She said cops had been chasing them, “sticking their middle fingers at us and screaming obscenities.’’

DeFerrari, 36, said the cops jumped out with “rifles drawn,’’ and, as they ordered, “Put your hands up,’’ Hamdy fired.

“There was no time to put your hands up at all,” said DeFerrari, a mom of three. “They shot in front of my face. Had I moved an inch, it would probably have been me.’’

She said the cop later said, “ ‘Your friend shot himself’ . . . I was in utter shock.’’ But “his hands were on the steering wheel at all times..”

Court records shows the city paid more than $225,000 both in 2001 and 2008 to people who sued Hamdy and other cops he was with for violating their rights. One was a Queens man who claimed he was beaten by cursing officers in 2007.

Polanco was a porter at a Honda dealership in Woodside, moonlighting handling hookah pipes at the Ice Lounge nightclub in Astoria.

He went to that bar to give DeFerrari a ride back to Lefrak City, where they both lived.

Polanco, whose dad recently committed suicide, also drove home her friend, Vanessa Rodriguez, 29 — an off-duty cop on modified duty who was busted in June for allegedly shoplifting. She said she was awakened by the gunfire.

Polanco began driving erratically, at one point cutting between two unmarked NYPD Emergency Service Unit vehicles in the center lane, cops said. Polanco then tailgated a car in the left lane, Browne said.

When the cops turned on their lights and sirens and ordered Polanco to “pull over” on their speakers, he sped up — even after a fearful DeFerrari asked him to slow down, Browne said.

When they finally stopped him, a sergeant jumped out of his car with Hamdy, 39.

Hamdy walked up to the open window on the passenger’s side and ordered the occupants to raise their hands, Browne said. Police sources claimed Polanco was reaching under his seat when Hamdy fired.

DeFerrari said of the pursuit, “I honestly thought it was an armored car . . . At no time did they specify that they were police.

When Hamdy fired, “I heard [Polanco] gasp. He just looked at me,” she said.

She said she told her friend’s mother, “I want you to know the truth. I was the last friendly face he saw as he was being dragged out like a dog.’’ When they were dragging him out,’’ she said, he was still alive. “He was looking at me.’’

At a vigil last night Polanco’s mom, Cecilia, said, “We’re going to make sure justice is done . . . He was my baby. Not a criminal. They took an innocent life.’’